Preheat oven to 350°F. Line a 9x9” pan with foil and spray with cooking spray.
Stir together oil, sugars, and eggs. Stir in cocoa, vanilla, cinnamon, salt and ground ginger. Slowly stir in flour. Stir in grated carrots.
Pour into prepared pan and bake 25-28 minutes. Cool before frosting.
To make frosting: Mix cream cheese and powdered sugar with a hand mixer. Add vanilla then add 1 tablespoon milk and mix until smooth adding up to 1 more tablespoon milk for desired consistency (whether you want to frost them vs drizzle as I did).
Start with regular carrots and shred them yourself - don't be tempted to start with pre-shredded carrots. Those are too thick and stiff for this recipe.
Don't pack your carrots, instead loosely add them to the cup. Using a heaping 1/2 cup is fine.
I used 2 tablespoons milk in the frosting as more of a drizzle, use less for thicker frosting.